This is what's known as a reduplicative or flip-flap word. In this case, a word is intensified in an informal way by doubling it up with a real word or a nonsense word that rhymes with it - like 'super duper' is an intensified form of 'super'. 'Easy-breezy' just means very easy indeed. Like George, I'm more familiar with 'easy peasy', and I'd never heard of 'easy-breezy' before, but it's clear what it means. In fact, it's a particularly expressive term, because it makes you think of the idiomatic phrase 'It's a breeze', which also means very easy.

It is usually "easy Peasee" which means it is very simple. e.g. Downloading an eBook is easy peasee.